Gayle has found chances hard to come by at Selhurst Park this season, and it is believed that Palace are chasing a striker in January.
Pardew has confirmed that the Eagles want to add a striker to their ranks in the coming weeks, and that arrival could knock Gayle even further down the pecking order.
The 24-year-old already appears to be behind Connor Wickham in the battle for places in Alan Pardew’s squad.
QPR, therefore, believe that they will be able to able to do a deal with Palace, to take the front man off their hands.
Rangers are looking for a player to partner Charlie Austin up front, as they have struggled for goals so far this season.
Gayle is currently out injured, but QPR are reportedly keen to force through a transfer when he returns to health.
Gayle has finished the last two seasons as Palace's top scorer and he has four goals to his name this term.